Decay of correlations in low density parity check codes: low noise regime

Authors:
Shrinivas Kudekar;Nicolas Macris
Affiliations:
Laboratory of theory of communications, School of Computer and Communication Sciences, EPFL, Lausanne;Laboratory of theory of communications, School of Computer and Communication Sciences, EPFL, Lausanne
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Year:
2009

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Abstract

Consider transmission over a binary additive white gaussian noise channel using a fixed low-density parity check code. We consider the posterior measure over the code bits and the corresponding correlation between two codebits, averaged over the noise realizations. We show that for low enough noise variance this average correlation decays exponentially fast with the graph distance between the code bits. One consequence of this result is that for low enough noise variance the GEXIT functions (further averaged over a standard code ensemble) of the belief propagation and optimal decoders are the same.